A model of the determinants of health combines three economic variables and two economic relationships.

For instance, the three economic variables are:

the amount a patient pays for a visit to a physiotherapist (P);

the number of times the patient visits the physiotherapist (V); and

the length of time it takes the patient to recover from a rotator cuff (shoulder) injury: (365 - D) days.

The two economic relationships are:

the number of visits (V) = 18 $0.09 (P).

In other words, if the price is zero, the patient will make 18 visits in order to receive treatment for this injury. If the price is $200, the patient will make zero visits.

the number of days to recover (365 D).

In this case, the number of healthy days (D) in the next year will be 180 + 5V. If the number of visits is zero, the patient will have 180 healthy days and it will take 185 (365 180) days to recover from the rotator cuff injury. If the number of visits is 18, the patient will have 270 [180 + 5(18)] healthy days, and the time to recover from the injury will be 95 days (365 270).

Use the above information to determine the relationship between price and health status in this model. In other words, solve for D and for P, and set up two equations: one showing the value of D in terms of P; and one showing the value of P in terms of D. Once you have determined the two equations, provide an interpretation of each equation.